Hits:

Indexed by:Journal Papers

Date of Publication:2015-12-01

Journal:MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Included Journals:SCIE、EI、Scopus

Volume:38

Issue:18,SI

Page Number:5048-5062

ISSN No.:0170-4214

Key Words:homoclinic orbit; fountain theorem; dual fountain theorem; damped differential equation

Abstract:We investigate the existence and multiplicity of homoclinic orbits for the second- order damped differential equations
   u+g(t)u - L(t)u +W-u(t,u) =0,
   where L(t) and W(t, u) are neither autonomous nor periodic in t. Under certain assumptions on g, L, andW, we get infinitely many homoclinic orbits for superquadratic, subquadratic and concave-convex nonlinearities cases by using fountain theoremand dual fountain theoremin critical point theory. These results generalize and improve some existing results in the literature. Copyright (C) 2015 JohnWiley & Sons, Ltd.